arXiv subjects

Matthias A. Müller

Publications and source records attributed to Matthias A. Müller.

At least 55 records · Page 3Linked to original sources

arXiv2025

Sufficient Conditions for Detectability of Approximately Discretized Nonlinear Systems

In many sampled-data applications, observers are designed based on approximately discretized models of continuous-time systems, where usually only the discretized system is analyzed in terms of its detectability. In this paper, we show that if the continuous-time system satisfies certain linear matrix inequality (LMI) conditions, and the sampling period of the discretization scheme is sufficiently small, then the whole family of discretized systems (parameterized by the sampling period) satisfies analogous discrete-time LMI conditions that imply detectability. Our results are applicable to general discretization schemes, as long as they produce approximate models whose linearizations are in some sense consistent with the linearizations of the continuous-time ones. We explicitly show that the Euler and second-order Runge-Kutta methods satisfy this condition. A batch-reactor system example is provided to highlight the usefulness of our results from a practical perspective.

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arXiv2025

Insights into the explainability of Lasso-based DeePC for nonlinear systems

Data-enabled Predictive Control (DeePC) has recently gained the spotlight as an easy-to-use control technique that allows for constraint handling while relying on raw data only. Initially proposed for linear time-invariant systems, several DeePC extensions are now available to cope with nonlinear systems. Nonetheless, these solutions mainly focus on ensuring the controller's effectiveness, overlooking the explainability of the final result. As a step toward explaining the outcome of DeePC for the control of nonlinear systems, in this paper, we focus on analyzing the earliest and simplest DeePC approach proposed to cope with nonlinearities in the controlled system, using a Lasso regularization. Our theoretical analysis highlights that the decisions undertaken by DeePC with Lasso regularization are unexplainable, as control actions are determined by data incoherent with the system's local behavior. This result is true even when the available input/output samples are grouped according to the different operating conditions explored during data collection. Our numerical study confirms these findings, highlighting the benefits of data grouping in terms of performance while showing that explainability remains a challenge in control design via DeePC.

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arXiv2025

Gaussian Processes with Noisy Regression Inputs for Dynamical Systems

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are typically noisy, which implies that both the regression inputs and outputs are corrupted by noise. However, most of the literature considers only noise in the regression outputs. In this paper, we show how to account for the noise in the regression inputs in an extended Gaussian process framework to approximate scalar and multidimensional systems. We demonstrate the potential of our framework by comparing it to different state-of-the-art methods in several simulation examples.

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arXiv2025

Multi-objective robust controller synthesis with integral quadratic constraints in discrete-time

This article presents a novel framework for the robust controller synthesis problem in discrete-time systems using dynamic Integral Quadratic Constraints (IQCs). We present an algorithm to minimize closed-loop performance measures such as the $\mathcal H_\infty$-norm, the energy-to-peak gain, the peak-to-peak gain, or a multi-objective mix thereof. While IQCs provide a powerful tool for modeling structured uncertainties and nonlinearities, existing synthesis methods are limited to the $\mathcal H_\infty$-norm, continuous-time systems, or special system structures. By minimizing the energy-to-peak and peak-to-peak gain, the proposed synthesis can be utilized to bound the peak of the output, which is crucial in many applications requiring robust constraint satisfaction, input-to-state stability, reachability analysis, or other pointwise-in-time bounds. Numerical examples demonstrate the robustness and performance of the controllers synthesized with the proposed algorithm.

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arXiv2025

Control Lyapunov Function Design via Configuration-Constrained Polyhedral Computing

This paper proposes novel approaches for designing control Lyapunov functions (CLFs) for constrained linear systems. We leverage recent configuration-constrained polyhedral computing techniques to devise piecewise affine convex CLFs. Additionally, we generalize these methods to uncertain systems with both additive and multiplicative disturbances. The proposed design methods are capable of approximating the infinite horizon cost function of both nominal and min-max optimal control problems by solving a single, one-stage, convex optimization problem. As such, these methods find practical applications in explicit controller design as well as in determining terminal regions and cost functions for nominal and min-max model predictive control (MPC). Numerical examples illustrate the effectiveness of this approach.

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arXiv2025

On discount functions for economic model predictive control without terminal conditions

In this paper, we investigate discounted economic model predictive control (E-MPC) schemes without terminal conditions in scenarios where the optimal operating behavior is a periodic orbit. For such a setting, it is known that a linearly discounted stage cost guarantees asymptotic stability of any arbitrarily small neighborhood of the optimal orbit if the prediction horizon is sufficiently long. However, in some examples very long prediction horizons are needed to achieve the desired performance. In this work, we extend these results by providing the same qualitative stability guarantees for a large class of discount functions. Numerical examples illustrate the influence of the discount function and show that with suitable discounting we can achieve significantly better performance than the linearly discounted E-MPC, even for short prediction horizons.

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arXiv2025

Modeling and Predictive Control for the Treatment of Hyperthyroidism

In this work, we propose an approach to determine the dosages of antithyroid agents to treat hyperthyroid patients. Instead of relying on a trial-and-error approach as it is commonly done in clinical practice, we suggest to determine the dosages by means of a model predictive control (MPC) scheme. To this end, we first extend a mathematical model of the pituitary-thyroid feedback loop such that the intake of methimazole, a common antithyroid agent, can be considered. Second, based on the extended model, we develop an MPC scheme to determine suitable dosages. In numerical simulations, we consider scenarios in which (i) patients are affected by Graves' disease and take the medication orally and (ii) patients suffering from a life-threatening thyrotoxicosis, in which the medication is usually given intravenously. Our conceptual study suggests that determining the medication dosages by means of an MPC scheme could be a promising alternative to the currently applied trial-and-error approach.

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arXiv2024

Polyhedral Control Design: Theory and Methods

In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers. In detail, we review the state-of-the-art techniques for computing geometric structures such as robust control invariant polytopes. Moreover, we survey recent methods for constructing control Lyapunov functions with polyhedral epigraphs as well as the extensive literature on robust model predictive control. The article concludes with a discussion of both the complexity and potential of polyhedral computing methods that rely on large-scale convex optimization.

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arXiv2024

An efficient data-based off-policy Q-learning algorithm for optimal output feedback control of linear systems

In this paper, we present a Q-learning algorithm to solve the optimal output regulation problem for discrete-time LTI systems. This off-policy algorithm only relies on using persistently exciting input-output data, measured offline. No model knowledge or state measurements are needed and the obtained optimal policy only uses past input-output information. Moreover, our formulation of the proposed algorithm renders it computationally efficient. We provide conditions that guarantee the convergence of the algorithm to the optimal solution. Finally, the performance of our method is compared to existing algorithms in the literature.

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arXiv2024

Data-Based System Representation and Synchronization for Multiagent Systems

This paper presents novel solutions of the data-based synchronization problem for continuous-time multiagent systems. We consider the cases of homogeneous and heterogeneous systems. First, we obtain a data-based representation of the synchronization error dynamics for homogeneous systems and show how to extend existing data-based stabilization results to stabilize such error dynamics. The proposed method relies on the solution of a set of linear matrix inequalities that are shown to be feasible. Then, we solve the synchronization problem for heterogeneous systems by means of dynamic controllers. Different from existing results, we do not require model knowledge for the followers and the leader. The theoretical results are finally validated using a numerical simulation.

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arXiv2024

Data-based system representations from irregularly measured data

Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult task. By exploiting the kernel structure of Hankel matrices of irregularly measured data generated by a linear time-invariant system, we provide computational methods for which any complete finite-length behavior of the system can be obtained. For the special case of periodically missing outputs, we provide conditions on the input such that the former result is guaranteed. In the presence of noise in the data, our method returns an approximate finite-length behavior of the system. We illustrate our result with several examples, including its use for approximate data completion in real-world applications and compare it to alternative methods.

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arXiv2024

Distributed MPC for Self-Organized Cooperation of Multiagent Systems -- Extended Version

We present a sequential distributed model predictive control (MPC) scheme for cooperative control of multi-agent systems with dynamically decoupled heterogeneous nonlinear agents subject to individual constraints. In the scheme, we explore the idea of using tracking MPC with artificial references to let agents coordinate their cooperation without external guidance. Each agent combines a tracking MPC with artificial references, the latter penalized by a suitable coupling cost. They solve an individual optimization problem for this artificial reference and an input that tracks it, only communicating the former to its neighbors in a communication graph. This puts the cooperative problem on a different layer than the handling of the dynamics and constraints, loosening the connection between the two. We provide sufficient conditions on the formulation of the cooperative problem and the coupling cost for the closed-loop system to asymptotically achieve it. Since the dynamics and the cooperative problem are only loosely connected, classical results from distributed optimization can be used to this end. We illustrate the scheme's application to consensus and formation control.

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arXiv2024

An input-output continuous-time version of Willems' lemma

We illustrate a novel version of Willems' lemma for data-based representation of continuous-time systems. The main novelties compared to previous works are two. First, the proposed framework relies only on measured input-output trajectories from the system and no internal (state) information is required. Second, our system representation makes use of exact system trajectories, without resorting to orthogonal bases representations and consequent approximations. We first establish sufficient and necessary conditions for data-based generation of system trajectories in terms of suitable latent variables. Subsequently, we reformulate these conditions using measured input-output data and show how to span the full behavior of the system. Furthermore, we show how to use the developed framework to solve the data-based continuous-time simulation problem.

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arXiv2024

Disturbance feedback-based model predictive control in uncertain dynamic environments

This paper presents a robust MPC scheme for linear systems subject to time-varying, uncertain constraints that arise from uncertain environments. The predicted input sequence is parameterized over future environment states to guarantee constraint satisfaction despite an imprecise environment prediction and unknown evolution of the future constraints. We provide theoretical guarantees for recursive feasibility and asymptotic convergence. Finally, a brief simulation example showcases our results.

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arXiv2024

Sample- and computationally efficient data-driven predictive control

Recently proposed data-driven predictive control schemes for LTI systems use non-parametric representations based on the image of a Hankel matrix of previously collected, persistently exciting, input-output data. Persistence of excitation necessitates that the data is sufficiently long and, hence, the computational complexity of the corresponding finite-horizon optimal control problem increases. In this paper, we propose an efficient data-driven predictive control (eDDPC) scheme which is both more sample efficient (requires less offline data) and computationally efficient (uses less decision variables) compared to existing schemes. This is done by leveraging an alternative data-based representation of the trajectories of LTI systems. We analytically and numerically compare the performance of this scheme to existing ones from the literature.

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arXiv2024

Robust Data-Driven Moving Horizon Estimation for Linear Discrete-Time Systems

In this paper, a robust data-driven moving horizon estimation (MHE) scheme for linear time-invariant discrete-time systems is introduced. The scheme solely relies on offline collected data without employing any system identification step. We prove practical robust exponential stability for the setting where both the online measurements and the offline collected data are corrupted by non-vanishing and bounded noise. The behavior of the novel robust data-driven MHE scheme is illustrated by means of simulation examples and compared to a standard model-based MHE scheme, where the model is identified using the same offline data as for the data-driven MHE scheme.

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arXiv2024

Robust stability of moving horizon estimation for continuous-time systems

We consider a moving horizon estimation (MHE) scheme involving a discounted least squares objective for general nonlinear continuous-time systems. Provided that the system is detectable (incrementally integral input/output-to-state stable, i-iIOSS), we show that there exists a sufficiently long estimation horizon that guarantees robust global exponential stability of the estimation error in a time-discounted $L^2$-to-$L^\infty$ sense. In addition, we show that i-iIOSS Lyapunov functions can be efficiently constructed by verifying certain linear matrix inequality conditions. In combination, we propose a flexible Lyapunov-based MHE framework in continuous time, which particularly offers more tuning possibilities than its discrete-time analog, and provide sufficient conditions for stability that can be easily verified in practice. Our results are illustrated by a numerical example.

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arXiv2024

Transient Performance of MPC for Tracking

We analyse the closed-loop performance of a model predictive control (MPC) for tracking formulation with artificial references. It has been shown that such a scheme guarantees closed-loop stability and recursive feasibility for any externally supplied reference, even if it is unreachable or time-varying. The basic idea is to consider an artificial reference as an additional decision variable and to formulate generalised terminal ingredients with respect to it. In addition, its offset is penalised in the MPC optimisation problem, leading to closed-loop convergence to the best reachable reference. In this paper, we provide a transient performance bound on the closed loop using MPC for tracking. We employ mild assumptions on the offset cost and scale it with the prediction horizon. In this case, an increasing horizon in MPC for tracking recovers the infinite horizon optimal solution.

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